Use the Traditional Method of Hypothesis Testing to Test the Given

question 7

Essay

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
-A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results are shown below. $\begin{array}{ c | r r r r r r r } \text { Subject } & A & B & C & D & E & F & G \\\hline \text { Before } & 9.4&9.5&9.7&9.4&9.5&9.7&9.6 \\\hline \text { After } &9.5&9.7&9.7&9.3&9.6&10&9.4\end{array}$
Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts' scores.

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Definitions:

Marginal External Cost

The cost imposed on a third party by the production of an additional unit of a good or service.

Production Efficiency

A level of output where a company cannot produce more of one good without reducing the output of another good, utilizing resources optimally.

Pollution Damage

The harmful impact of pollutants on the environment, human health, and the economy.

Marginal Social Cost

The cumulative expense incurred by society for creating one more unit of a product or service, encompassing both direct private costs and any external effects.